### Home > MC1 > Chapter 9 > Lesson 9.3.2 > Problem9-137

9-137.

When writing numbers that are approximate, it is possible to use different degrees of accuracy.

If you are instructed to be accurate to the nearest tenth, your answer should be the closest approximation using tenths. For example, you would approximate $5.248962$ as $5.2$, because the digit in the hundredths place is less than 5. You would approximate $10.396$ as $10.4$, because the digit in the hundredths place is greater than or equal to $5$.

If you are instructed to be accurate to the nearest hundredth, your answer should be the closest approximation using hundredths. For example, you would approximate $5.248962$ as $5.25$ and $10.396$ as $10.40$, based on the digit in the thousandths place.

Express each of the following numbers as approximations to the given degrees of accuracy.

1. Write $12.6243258$ accurately to the nearest tenth.

You only need to look at the hundredths place, since that will determine how to round the tenths place.

Since the hundredths place is a $2$, you round down.
The correct answer is $12.6$.

2. Write $0.119834$ accurately to the nearest hundredth.

What number is in the thousandths place?
What is the nearest hundredth?

$0.12$

3. Write $π$ accurately to the nearest ten-thousandth.

The ten-thousandth place is the fourth number after the decimal.