Decimal Place Value: Practice

Two digits after the point means the denominator is $100$. Then reduce by the greatest common factor, which is $25$.

$0.25 = \frac{25}{100} = \frac{1}{4}$

The $2$ is ones, the $0$ is tenths, and the $8$ is hundredths. The placeholder zero adds nothing but holds the tenths place.

$2.08 = 2 + \frac{0}{10} + \frac{8}{100} = 2 + \frac{8}{100}$

The last digit, $1$, is in the hundredths place, and the last place names the fraction.

$0.41 = \frac{41}{100}$

So $0.41$ reads "forty-one hundredths."

One digit after the point means the denominator is $10$. Then reduce by the greatest common factor, which is $2$.

$0.6 = \frac{6}{10} = \frac{3}{5}$

A denominator of $100$ means the digits fill two places after the point, so the string "37" lands in the tenths and hundredths places.

$\frac{37}{100} = 0.37$

The $7$ is ones, $3$ is tenths, $0$ is hundredths, and $5$ is thousandths. The placeholder zero in the hundredths place contributes nothing.

$7.305 = 7 + \frac{3}{10} + \frac{0}{100} + \frac{5}{1000} = 7 + \frac{3}{10} + \frac{5}{1000}$

One digit after the point means the denominator is $10$. Then reduce by the greatest common factor, which is $2$.

$0.8 = \frac{8}{10} = \frac{4}{5}$

A zero on the far right does not change a decimal's value, so padding $0.45$ with a trailing zero gives $0.450$.

$0.45 = 0.450$

So the two decimals are equal.

Read the whole part, say "and" for the point, then read the fractional part with its last place name. The $6$ is in the tenths place.

$5.6 = 5 + \frac{6}{10}$

So $5.6$ reads "five and six tenths."

Two digits after the point means the denominator is $100$. Then reduce by the greatest common factor of $5$ and $100$, which is $5$.

$0.05 = \frac{5}{100} = \frac{1}{20}$

Pad each to two places and compare from the left: $0.45$, $0.50$, $0.54$. The tenths digits are $4$, $5$, $5$, and the two with $5$ tenths split on the hundredths.

$0.45 < 0.50 < 0.54$

The first $6$ is in the tenths place (value $\tfrac{6}{10}$) and the second $6$ is in the hundredths place (value $\tfrac{6}{100}$). Each place is ten times the place to its right.

$\frac{6/10}{6/100} = \frac{6}{10} \times \frac{100}{6} = 10$

So the first $6$ is worth $10$ times the second.