Which expanded form is correct for 30.508?

Class 6DecimalsDecimals

A $3 + \frac{5}{10} + \frac{8}{100}$
B $30 + \frac{5}{100} + \frac{8}{1000}$
C $30 + \frac{50}{100} + \frac{8}{100}$
D $30 + \frac{5}{10} + \frac{8}{1000}$

Step-by-Step Solution

30.508 is 3 tens + 0 ones + 5 tenths + 0 hundredths + 8 thousandths, which is

30 + \frac{5}{10} + \frac{8}{1000}

. The zero in the hundredths place adds nothing but must still hold its place — treating the 8 as hundredths turns the number into 30.58.

Answer: D)

30 + \frac{5}{10} + \frac{8}{1000}

Key idea: Place value to the right of the decimal point

To the LEFT of the decimal point: ones, tens, hundreds — each place is **10 times** bigger than the one to its right. To the RIGHT of the decimal point, the same rule continues — each place is **10 times smaller** than the one to its left. So:

- 1st place after the point: tenths (1/10)
- 2nd place: hundredths (1/100)
- 3rd place: thousandths (1/1000)

The decimal

23.456 = 2 \times 10 + 3 \times 1 + 4 \times (1/10) + 5 \times (1/100) + 6 \times (1/1000)

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