// Numbas version: exam_results_page_options
{"name": "multiplying and dividing with decimals", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"rand": {"definition": "random(1..4)", "type": "number", "parameters": [], "language": "jme"}}, "ungrouped_variables": ["numa1", "numa2", "numb1", "numb2", "ans1", "ans2", "numc1", "numc2", "ans3", "numd1", "numd2", "ans4", "d3", "d1", "d2", "e3", "e1", "e2", "f3", "f1", "f2", "g3", "g1", "g2", "h3", "h1", "h2", "sig", "dec", "rand1", "rand2", "rand3", "rand4", "rand5"], "name": "multiplying and dividing with decimals", "tags": ["decimal", "rebel", "Rebel", "REBEL", "rebelmaths"], "advice": "<p><span style=\"text-decoration: underline;\"><strong>When multipling using decimals</strong></span></p>\n<p>When multipling using decimals, count how many decimal places you need to move the number to make it a whole number e.g</p>\n<p>0.000054 to get to 54, we moved 6 decimal places and 0.004 to get to 4, we moved 3 decimal places</p>\n<p>So if we want to do $0.000054 \\times 0.004$ =&gt; we move the first number 6 decimal places and the second number 3 decimal places</p>\n<p>=&gt; $54 \\times 4 = 216$</p>\n<p>Now since we moved 9 decimal places, altogether to the right, we move the answer 9 decimals places back to the left i.e.</p>\n<p>216 becomes 0.000000216</p>\n<p></p>\n<p><span style=\"text-decoration: underline;\"><strong>When rounding to a given number of decimal places</strong></span></p>\n<p>When rounding to a given number of decimal places, do the following</p>\n<p>Look at the next number after the last number of the decimal places you need to round to</p>\n<p>If the number is 5 or greater, round up, if it is than 5, leave as is; i.e.</p>\n<p>round to 3 decimal places the following</p>\n<p>$0.0055 = 0.006$</p>\n<p>$0.0071 = 0.007$</p>\n<p></p>\n<p><span style=\"text-decoration: underline;\"><strong>When rounding to a given number of significant&nbsp;figures</strong></span></p>\n<p>When rounding to a given number of significant figures, do the following</p>\n<p>Look at the next number after the last number of the significant figuresyou need to round to</p>\n<p>If the number is 5 or greater, round up, if it is than 5, leave as is; i.e.</p>\n<p>N.B. Remember to keep the number you rounded to the significant number of places in the same unit e.g. 10's, 100's etc</p>\n<p>round to 3 significant figures the following</p>\n<p>$2573 = 2570$</p>\n<p>$7828 = 7830$</p>\n<p>round to&nbsp;1 significant figures the following</p>\n<p>$15 = 20$</p>\n<p>$38851 = 40000$</p>", "rulesets": {}, "parts": [{"prompt": "<p>$\\var{numa1} \\times \\var{numa2}$</p>\n<p>[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans1}", "minValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\var{numb1} \\times&nbsp;\\var{numb2}$</p>\n<p>[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans2}", "minValue": "{ans2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\var{numc1} \\times&nbsp;\\var{numc2}$</p>\n<p>[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans3}", "minValue": "{ans3}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\var{d3}&nbsp;\\div \\var{d1}$</p>\n<p>[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{d2}", "minValue": "{d2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\var{e3}&nbsp;\\div \\var{e1}$</p>\n<p>[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{e2}", "minValue": "{e2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\var{f3}&nbsp;\\div \\var{f1}$</p>\n<p>[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{f2}", "minValue": "{f2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\var{g3}&nbsp;\\div \\var{g1}$</p>\n<p>[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{g2}", "minValue": "{g2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\var{h3}&nbsp;\\div \\var{h1}$</p>\n<p>[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{h2}", "minValue": "{h2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>Evaluate each of the following without using a calculator:</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"f1": {"definition": "random(0.0022..0.0049#0.0001)  ", "templateType": "anything", "group": "Ungrouped variables", "name": "f1", "description": ""}, "f2": {"definition": "random(50000..100000#0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "f2", "description": ""}, "f3": {"definition": "f1*f2", "templateType": "anything", "group": "Ungrouped variables", "name": "f3", "description": ""}, "numa2": {"definition": "random(0.11..0.19#0.01)", "templateType": "anything", "group": "Ungrouped variables", "name": "numa2", "description": ""}, "numa1": {"definition": "random(0.0011..0.0035)", "templateType": "anything", "group": "Ungrouped variables", "name": "numa1", "description": ""}, "h2": {"definition": "random(1.225..1.975#0.05)  ", "templateType": "anything", "group": "Ungrouped variables", "name": "h2", "description": ""}, "ans1": {"definition": "numa1*numa2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ans2": {"definition": "numb1*numb2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "ans3": {"definition": "numc1*numc2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}, "ans4": {"definition": "numd1*numd2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans4", "description": ""}, "numc1": {"definition": "random(1.2..1.4#0.01)", "templateType": "anything", "group": "Ungrouped variables", "name": "numc1", "description": ""}, "numc2": {"definition": "random(0.0011..0.0059#0.0001)", "templateType": "anything", "group": "Ungrouped variables", "name": "numc2", "description": ""}, "d2": {"definition": "random(50.5..69.5#0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "d2", "description": ""}, "d3": {"definition": "d1*d2", "templateType": "anything", "group": "Ungrouped variables", "name": "d3", "description": ""}, "d1": {"definition": "random(0.2..0.8#0.1)", "templateType": "anything", "group": "Ungrouped variables", "name": "d1", "description": ""}, "sig": {"definition": "random(800..2000#0.0001)  ", "templateType": "anything", "group": "Ungrouped variables", "name": "sig", "description": ""}, "h3": {"definition": "h1*h2", "templateType": "anything", "group": "Ungrouped variables", "name": "h3", "description": ""}, "numb2": {"definition": "random(0.002..0.009#0.001)", "templateType": "anything", "group": "Ungrouped variables", "name": "numb2", "description": ""}, "numb1": {"definition": "random(0.000033..0.000079#0.000001)", "templateType": "anything", "group": "Ungrouped variables", "name": "numb1", "description": ""}, "h1": {"definition": "random(0.0022..0.0055#0.000001)  ", "templateType": "anything", "group": "Ungrouped variables", "name": "h1", "description": ""}, "g3": {"definition": "g1*g2", "templateType": "anything", "group": "Ungrouped variables", "name": "g3", "description": ""}, "g2": {"definition": "random(0.0022..0.0049#0.0001)  ", "templateType": "anything", "group": "Ungrouped variables", "name": "g2", "description": ""}, "g1": {"definition": "random(21.1..31.1#0.2)  ", "templateType": "anything", "group": "Ungrouped variables", "name": "g1", "description": ""}, "numd1": {"definition": "random(20.1..91.1#0.2)", "templateType": "anything", "group": "Ungrouped variables", "name": "numd1", "description": ""}, "numd2": {"definition": "random(0.0201..0.0299#0.0002)", "templateType": "anything", "group": "Ungrouped variables", "name": "numd2", "description": ""}, "e1": {"definition": "random(0.0002..0.0009)", "templateType": "anything", "group": "Ungrouped variables", "name": "e1", "description": ""}, "e3": {"definition": "e1*e2", "templateType": "anything", "group": "Ungrouped variables", "name": "e3", "description": ""}, "e2": {"definition": "random(50000..100000#0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "e2", "description": ""}, "rand1": {"definition": "rand()", "templateType": "anything", "group": "Ungrouped variables", "name": "rand1", "description": ""}, "rand2": {"definition": "random(1..4 except {rand1})", "templateType": "anything", "group": "Ungrouped variables", "name": "rand2", "description": ""}, "rand3": {"definition": "rand()", "templateType": "anything", "group": "Ungrouped variables", "name": "rand3", "description": ""}, "dec": {"definition": "random(0.0001..0.0009#0.0000001)  ", "templateType": "anything", "group": "Ungrouped variables", "name": "dec", "description": ""}, "rand4": {"definition": "random(1..4 except{rand3})", "templateType": "anything", "group": "Ungrouped variables", "name": "rand4", "description": ""}, "rand5": {"definition": "random(1..4 except {rand4} except{rand3})", "templateType": "anything", "group": "Ungrouped variables", "name": "rand5", "description": ""}}, "metadata": {"description": "<p>Multiplying and dividing decimals</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}]}