Round each decimal number to the given place value. a) 5.38 to the nearest tenth b) 103.843 to the nearest hundredth
The correct answer and explanation is:
Sure! Here are the answers first, then the explanation:
a) 5.38 rounded to the nearest tenth
Look at the hundredths place (second digit after the decimal).
5.38 → Tenths digit = 3, Hundredths digit = 8
Since 8 ≥ 5, round the tenths digit up from 3 to 4.
Answer: 5.4
b) 103.843 rounded to the nearest hundredth
Look at the thousandths place (third digit after the decimal).
103.843 → Hundredths digit = 4, Thousandths digit = 3
Since 3 < 5, do not round up.
Answer: 103.84
Explanation:
Rounding decimals involves looking at the digit immediately to the right of the place value you want to round to and deciding whether to increase the digit or leave it as is.
- If the digit to the right is 5 or greater, you increase the rounding digit by 1.
- If the digit to the right is less than 5, you leave the rounding digit the same.
a) Rounding 5.38 to the nearest tenth:
- The tenths place is the first digit after the decimal point — here it’s 3.
- The next digit, the hundredths place, is 8.
- Because 8 is greater than 5, we increase the tenths digit by 1 (3 + 1 = 4).
- The digits after the tenths place are dropped.
- Result: 5.4
b) Rounding 103.843 to the nearest hundredth:
- The hundredths place is the second digit after the decimal point — here it’s 4.
- The next digit, the thousandths place, is 3.
- Since 3 is less than 5, we keep the hundredths digit as 4.
- All digits beyond the hundredths place are dropped.
- Result: 103.84
Why is rounding important?
Rounding helps simplify numbers, making them easier to work with and communicate, especially when exact precision is not necessary. For example, financial transactions often round to the nearest cent (hundredth place), while measurements might round to the nearest tenth for easier reading.
By following the basic rounding rule—looking at the digit immediately right of your place value—you can round any decimal number correctly!