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AUTO MECHANICS While doing a tune-up, a mechanic checks the gap on one of the spark plugs of a car to be sure it is firing correctly. The owner's manual states that the gap should be $\frac{2}{125}$ inch. The gauge the mechanic uses to check the gap is in decimal notation; it registers 0.025 inch. Is the spark plug gap too large or too small?

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$0.009 \mathrm{in}$

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Chapter 5

Decimals

Section 5

Fractions and Decimals

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we have a gap which should be to over 125 inches. What it is measured at 1250.25 inches. So is the gap to bigger? Too small. To find this out, we have to convert one of these things to the other ones. Notation that is, either this into decimals or vice versa. So in this case, I'm going toe opt to convert this decimal into a fraction. That is, if we multiply it by 1000 over 1000 we will get 25 over 1000 inches now. It's not very useful now because we can't compare fractions in this state, that is, the denominators are different, so we're going to take the left most fraction and multiply so it's denominator equals 1000. That is, if we multiply by 8/8, we will get eight times two is 16 over eight times 125 is 1000. So which of these is greater? Well, it's definitely the 25 over 1000 that's greater than the 16 over 1000 meaning the current gap is in fact, two large that is, 3500 is much larger than the desired gap size of 16 over 1000 inches

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