In the number 135.792, what value is repre-sented by the 9?
a. 90
b. nine tenths
c. nine one-hundredths
d. nine one-thousandths
The correct answer and explanation is:
The correct answer is c. nine one-hundredths.
Here’s the breakdown:
In a decimal number, the place value of each digit is determined by its position relative to the decimal point. The number 135.792 has the following digits and places:
- 1 is in the hundreds place (100),
- 3 is in the tens place (10),
- 5 is in the ones place (1),
- 7 is in the tenths place (0.1),
- 9 is in the hundredths place (0.01),
- 2 is in the thousandths place (0.001).
So, the 9 is in the hundredths place, which represents nine one-hundredths or 0.09.
To clarify, the place values for decimal digits are:
- The tenths place represents tenths, or one-tenth (0.1),
- The hundredths place represents hundredths, or one-hundredth (0.01),
- The thousandths place represents thousandths, or one-thousandth (0.001).
Since the 9 is in the hundredths place, it represents nine one-hundredths (0.09). Therefore, the correct answer is option c.
This explanation shows how the decimal system is based on powers of ten. As you move to the right of the decimal point, each place value represents a fraction of ten (tenths, hundredths, thousandths, etc.). Each digit’s place tells you how many of that fraction are present in the number.