Recognizing decimal places

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Questions 1 - 3

Examine the decimal

What is the place value of the position occupied by the "7"?

Thousandths

Tenths

Hundredths

Ten-thousandths

Explanation

After the decimal point, the place values of the digits are, in order:

$\frac{1}{10^1} = \frac{1}{10}$

$\frac{1}{10^2} = \frac{1}{100}$

$\frac{1}{10^3} = \frac{1}{1,000}$

$\frac{1}{10^4} = \frac{1}{10,000}$ ...

The "7" is in the third place after the decimal point, so its place value is one thousandth.

The number 0.045 is equal to which of the following?

Forty-five one-thousandths

Forty-five one-hundredths

Forty-five ten-thousandths

Four hundred five one-thousandths

Four hundred five ten-thousandths

Explanation

After the decimal point, the place values of the digits are, in order:

$\frac{1}{10^1} = \frac{1}{10}$

$\frac{1}{10^2} = \frac{1}{100}$

$\frac{1}{10^3} = \frac{1}{1,000}$

The last nonzero digit of 0.045 appears in that third place, so the fractional form of this decimal expression is $\frac{45}{1,000}$ , or forty-five one-thousandths.

Which of the following is equal to six hundred seven ten-thousandths?

Explanation

"Six hundred seven ten-thousandths" is the fraction $\frac{607}{10,000}$ . To write this in decimal form, put the "7" in the ten-thousandths place, which is the fourth place after the decimal point. This number is "0.0607."

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