Math CentralQuandaries & Queries


Question from seth, a student:

A decimal number rounded changed to 23.7 after it was rounded.
Give a decimal number that is less than 23.7 and another that is greater than 23.7 that each round to 23.7.
Explain to what place each number was rounded.

Hi Seth,

Let me try with the same instructions, but with, 56.74 as the number. If you are having difficulties with the place value names have a look at our place value table.

In my number 56.74, the digit 4 is in the hundredths place so if this is the result of my rounding then I was rounding to the hundredths place. Suppose I start with 56.74?x where ? is some digit and x is a string of digits. For example I might start with 56.743 or 56.744986 or 56.748 and want to round to the hundredths place. The first step is to ignore any digits to the right of the thousandths place so the numbers I am left with are 56.743, 56.744, and 56.748.

The next step is to look at the digit in the thousandths place. If it is less than 5 you just drop the thousandths digit and report 56.74. This is the situation in my first two numbers, 56.743 and 56.744. If however the thousandths digit is 5 or more you increase the hundredths digit by 1 and drop the thousandths digit. Hence 56.748 rounds to 56.75.

The one complication that can arise is with a 9 in the hundredths place. Suppose you have 23.497 and you want to round to the hundredths place. Since the 7 in the thousands place is greater than 5 you need to increase the hundredths digit by 1. But 9 + 1 = 10 so 23.497, rounded to the hundredths place is 23.50.

I hope this helps,

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