To write decimals in expanded form, we break the number down by the place value of each digit.
Here is how the place values work:
*
Left of the decimal point: Ones, Tens, Hundreds, Thousands, etc.
*
Right of the decimal point: Tenths ($0.1$), Hundredths ($0.01$), Thousandths ($0.001$), Ten-thousandths ($0.0001$).
Let's solve each problem step-by-step:
1) 4.38
* The $4$ is in the ones place: $4$
* The $3$ is in the tenths place: $0.3$
* The $8$ is in the hundredths place: $0.08$
*
Answer: $4 + 0.3 + 0.08$
2) 23.734
* The $2$ is in the tens place: $20$
* The $3$ is in the ones place: $3$
* The $7$ is in the tenths place: $0.7$
* The $3$ is in the hundredths place: $0.03$
* The $4$ is in the thousandths place: $0.004$
*
Answer: $20 + 3 + 0.7 + 0.03 + 0.004$
3) 14,758 (Note: There is no decimal point shown, so this is a whole number)
* The $1$ is in the ten-thousands place: $10,000$
* The $4$ is in the thousands place: $4,000$
* The $7$ is in the hundreds place: $700$
* The $5$ is in the tens place: $50$
* The $8$ is in the ones place: $8$
*
Answer: $10,000 + 4,000 + 700 + 50 + 8$
4) 9752.18
* The $9$ is in the thousands place: $9,000$
* The $7$ is in the hundreds place: $700$
* The $5$ is in the tens place: $50$
* The $2$ is in the ones place: $2$
* The $1$ is in the tenths place: $0.1$
* The $8$ is in the hundredths place: $0.08$
*
Answer: $9,000 + 700 + 50 + 2 + 0.1 + 0.08$
5) 17.945
* The $1$ is in the tens place: $10$
* The $7$ is in the ones place: $7$
* The $9$ is in the tenths place: $0.9$
* The $4$ is in the hundredths place: $0.04$
* The $5$ is in the thousandths place: $0.005$
*
Answer: $10 + 7 + 0.9 + 0.04 + 0.005$
6) 39.45
* The $3$ is in the tens place: $30$
* The $9$ is in the ones place: $9$
* The $4$ is in the tenths place: $0.4$
* The $5$ is in the hundredths place: $0.05$
*
Answer: $30 + 9 + 0.4 + 0.05$
7) 2.42
* The $2$ is in the ones place: $2$
* The $4$ is in the tenths place: $0.4$
* The $2$ is in the hundredths place: $0.02$
*
Answer: $2 + 0.4 + 0.02$
8) 23.358
* The $2$ is in the tens place: $20$
* The $3$ is in the ones place: $3$
* The $3$ is in the tenths place: $0.3$
* The $5$ is in the hundredths place: $0.05$
* The $8$ is in the thousandths place: $0.008$
*
Answer: $20 + 3 + 0.3 + 0.05 + 0.008$
9) 1843.42
* The $1$ is in the thousands place: $1,000$
* The $8$ is in the hundreds place: $800$
* The $4$ is in the tens place: $40$
* The $3$ is in the ones place: $3$
* The $4$ is in the tenths place: $0.4$
* The $2$ is in the hundredths place: $0.02$
*
Answer: $1,000 + 800 + 40 + 3 + 0.4 + 0.02$
10) 3.8225
* The $3$ is in the ones place: $3$
* The $8$ is in the tenths place: $0.8$
* The $2$ is in the hundredths place: $0.02$
* The $2$ is in the thousandths place: $0.002$
* The $5$ is in the ten-thousandths place: $0.0005$
*
Answer: $3 + 0.8 + 0.02 + 0.002 + 0.0005$
Final Answer:
1) $4 + 0.3 + 0.08$
2) $20 + 3 + 0.7 + 0.03 + 0.004$
3) $10,000 + 4,000 + 700 + 50 + 8$
4) $9,000 + 700 + 50 + 2 + 0.1 + 0.08$
5) $10 + 7 + 0.9 + 0.04 + 0.005$
6) $30 + 9 + 0.4 + 0.05$
7) $2 + 0.4 + 0.02$
8) $20 + 3 + 0.3 + 0.05 + 0.008$
9) $1,000 + 800 + 40 + 3 + 0.4 + 0.02$
10) $3 + 0.8 + 0.02 + 0.002 + 0.0005$
Parent Tip: Review the logic above to help your child master the concept of expanded notation with decimals worksheet.
