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first non-zero digit

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Use the drop-down menu to create the correct sentence.

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If you are unsure of how to do a question, click on Show steps to see the full working. Then, once you understand how to do the question, click on Try another question like this one to start again.

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The trailing zeros do not change the value of a decimal. In the same way that $42$ is no different to $000042$ (regardless of how many zeros are placed at the front), $\\var{trailshort}$ is no different to $\\var{trailshort}0000$ (regardless of how many zeros are placed at the back). This is why it is important to read things such as $0.200$ as \"zero point two zero zero\" and not as \"zero point two hundred\".

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In general, the length or number of digits in a decimal does not tell us anything about how big the decimal is. The only things that affect the actual value of a decimal are the non-zero digits and their placement relative to the decimal point (that is their face value and place value).

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The number {trail[0]} is [[0]] {trail[1]}

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You may have suspected that $\\var{fnz[0]}$ was greater than $\\var{fnz[1]}$ simply because $\\var{fnzdigbig}$ was greater than $\\var{fnzdigsmall}$, however, $\\var{fnzdigbig}$ is in a column with a smaller place value!

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You may have suspected that $\\var{fnz[0]}$ was less than $\\var{fnz[1]}$ simply because $\\var{fnzdigsmall}$ was less than $\\var{fnzdigbig}$, however, $\\var{fnzdigsmall}$ is in a column with a larger place value!

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In general, the first non-zero digit does not tell us anything about how big the decimal is. The only things that affect the actual value of a decimal are the non-zero digits and their placement relative to the decimal point (that is their face value and place value).

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You can add zeros so that the decimals have the same number of decimals places, and then, comparing them might be easier. That is, by appending a zero (which doesn't affect the value) onto the end of $\\var{fnzdigsmall/10}$ it might be clearer that $\\var{fnzdigsmall/10}0$ is greater than $\\var{fnzdigbig/100}$. Note that $\\var{fnzdigsmall/10}0$ is $\\var{fnzdigsmall}0$ hundredths whereas $\\var{fnzdigbig/100}$ is $\\var{fnzdigbig}$ hundredths.

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The number $\\var{fnz[0]}$ is [[0]] $\\var{fnz[1]}$

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Some students believe a decimal is larger if it is longer, some believe a decimal is larger if its first non-zero digit is larger.

"}, "advice": "

If you are unsure of how to do a question, click on Show steps to see the full working. Then, once you understand how to do the question, click on Try another question like this one to start again.

", "type": "question", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}