Decimal Place Values 1

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Year 10

Decimals

Decimal Place Values

Decimal Place Values 1

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Question 1 of 5

1. Question
Convert to expanded form

$14.305$ $14.305$
- 1. $(1 \times 10) + (4 \times 1) + (3 \times \frac{1}{1}) + (5 \times \frac{1}{100})$ $(1xx10)+(4xx1)+(3xx1/1)+(5xx1/100)$
- 2. $(1 \times 100) + (4 \times 10) + (3 \times \frac{1}{1}) + (5 \times \frac{1}{100})$ $(1xx100)+(4xx10)+(3xx1/1)+(5xx1/100)$
- 3. $(1 \times 100) + (4 \times 10) + (3 \times \frac{1}{100}) + (5 \times \frac{1}{1000})$ $(1xx100)+(4xx10)+(3xx1/100)+(5xx1/1000)$
- 4. $(1 \times 10) + (4 \times 1) + (3 \times \frac{1}{10}) + (5 \times \frac{1}{1000})$ $(1xx10)+(4xx1)+(3xx1/10)+(5xx1/1000)$
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The expanded form of a decimal is the sum of its digits multiplied to their place values and are separated by parentheses.

$Place Values$ $\text(Place Values)$

Hundreds Tens Units $.$ $.$ Tenths Hundredths Thousandths

$100$ $100$ $10$ $10$ $1$ $1$ $.$ $.$ $\frac{1}{10}$ $1/10$ $\frac{1}{100}$ $1/100$ $\frac{1}{1000}$ $1/1000$

Match the given values to the corresponding place values in the table.

$14.305$ $14.305$

$Place Values$ $\text(Place Values)$

Tens Units $.$ $.$ Tenths Hundredths Thousandths

$10$ $10$ $1$ $1$ $.$ $.$ $\frac{1}{10}$ $1/10$ $\frac{1}{100}$ $1/100$ $\frac{1}{1000}$ $1/1000$

$1$ $1$ $4$ $4$ $.$ $.$ $3$ $3$ $0$ $0$ $5$ $5$

Next, multiply the corresponding digits to their place values, starting from the left side, and get their sum.

Each product should be separated by a parenthesis

$Tens$ $\text(Tens)$ $= 1 \times 10$ $=1xx10$

$Units$ $\text(Units)$ $= 4 \times 1$ $=4xx1$

$Tenths$ $\text(Tenths)$ $= 3 \times \frac{1}{10}$ $=3xx1/10$

$Hundredths$ $\text(Hundredths)$ $= 0 \times \frac{1}{100} = 0$ $=0xx1/100=0$

$Thousandths$ $\text(Thousandths)$ $= 5 \times \frac{1}{1000}$ $=5xx1/1000$

$14.305$ $14.305$ $=$ $=$ $(1 \times 10) + (4 \times 1) + (3 \times \frac{1}{10}) + (5 \times \frac{1}{1000})$ $(1xx10)+(4xx1)+(3xx1/10)+(5xx1/1000)$

$(1 \times 10) + (4 \times 1) + (3 \times \frac{1}{10}) + (5 \times \frac{1}{1000})$ $(1xx10)+(4xx1)+(3xx1/10)+(5xx1/1000)$
Question 2 of 5

2. Question
Convert to expanded form

$401.521$ $401.521$
- 1. $(4 \times 100) + (1 \times 10) + (5 \times 1) + (2 \times \frac{1}{100}) + (1 \times \frac{1}{1000})$ $(4xx100)+(1xx10)+(5xx1)+(2xx1/100)+(1xx1/1000)$
- 2. $(4 \times 100) + (1 \times 1) + (5 \times \frac{1}{10}) + (2 \times \frac{1}{100}) + (1 \times \frac{1}{1000})$ $(4xx100)+(1xx1)+(5xx1/10)+(2xx1/100)+(1xx1/1000)$
- 3. $(4 \times 100) + (1 \times 10) + (5 \times 1) + (2 \times \frac{1}{10}) + (1 \times \frac{1}{100})$ $(4xx100)+(1xx10)+(5xx1)+(2xx1/10)+(1xx1/100)$
- 4. $(4 \times 1000) + (1 \times 100) + (5 \times 10) + (2 \times \frac{1}{10}) + (1 \times \frac{1}{100})$ $(4xx1000)+(1xx100)+(5xx10)+(2xx1/10)+(1xx1/100)$
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The expanded form of a decimal is the sum of its digits multiplied to their place values and are separated by parentheses.

$Place Values$ $\text(Place Values)$

Hundreds Tens Units $.$ $.$ Tenths Hundredths Thousandths

$100$ $100$ $10$ $10$ $1$ $1$ $.$ $.$ $\frac{1}{10}$ $1/10$ $\frac{1}{100}$ $1/100$ $\frac{1}{1000}$ $1/1000$

Match the given values to the corresponding place values in the table.

$401.521$ $401.521$

$Place Values$ $\text(Place Values)$

Hundreds Tens Units $.$ $.$ Tenths Hundredths Thousandths

$100$ $100$ $10$ $10$ $1$ $1$ $.$ $.$ $\frac{1}{10}$ $1/10$ $\frac{1}{100}$ $1/100$ $\frac{1}{1000}$ $1/1000$

$4$ $4$ $0$ $0$ $1$ $1$ $.$ $.$ $5$ $5$ $2$ $2$ $1$ $1$

Next, multiply the corresponding digits to their place values, starting from the left side, and get their sum.

Each product should be separated by a parenthesis

$Hundreds$ $\text(Hundreds)$ $= 4 \times 100$ $=4xx100$

$Tens$ $\text(Tens)$ $= 0 \times 10 = 0$ $=0xx10=0$

$Units$ $\text(Units)$ $= 1 \times 1$ $=1xx1$

$Tenths$ $\text(Tenths)$ $= 5 \times \frac{1}{10}$ $=5xx1/10$

$Hundredths$ $\text(Hundredths)$ $= 2 \times \frac{1}{100}$ $=2xx1/100$

$Thousandths$ $\text(Thousandths)$ $= 1 \times \frac{1}{1000}$ $=1xx1/1000$

$401.521$ $401.521$ $=$ $=$ $(4 \times 100) + (1 \times 1) + (5 \times \frac{1}{10}) + (2 \times \frac{1}{100}) + (1 \times \frac{1}{1000})$ $(4xx100)+(1xx1)+(5xx1/10)+(2xx1/100)+(1xx1/1000)$

$(4 \times 100) + (1 \times 1) + (5 \times \frac{1}{10}) + (2 \times \frac{1}{100}) + (1 \times \frac{1}{1000})$ $(4xx100)+(1xx1)+(5xx1/10)+(2xx1/100)+(1xx1/1000)$
Question 3 of 5

3. Question
Convert to a decimal

$73 + \frac{2}{10} + \frac{9}{1000}$ $73+2/10+9/1000$
- (73.209)
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To convert from expanded form to decimal form, use a table of place values to match the given values to their corresponding place value

$Place Values$ $\text(Place Values)$

Hundreds Tens Units $.$ $.$ Tenths Hundredths Thousandths

$100$ $100$ $10$ $10$ $1$ $1$ $.$ $.$ $\frac{1}{10}$ $1/10$ $\frac{1}{100}$ $1/100$ $\frac{1}{1000}$ $1/1000$

Match the given values to the corresponding place values in the table.

If there is no corresponding digit for a place value, write $0$ $0$ .

$7$ $7$ $3$ $3$ $+$ $+$ $\frac{2}{10}$ $2/10$ $+$ $+$ $\frac{9}{1000}$ $9/1000$

Tens Units $.$ $.$ Tenths Hundredths Thousandths

$10$ $10$ $1$ $1$ $.$ $.$ $\frac{1}{10}$ $1/10$ $\frac{1}{100}$ $1/100$ $\frac{1}{1000}$ $1/1000$

$7$ $7$ $3$ $3$ $.$ $.$ $2$ $2$ $0$ $0$ $9$ $9$

$=$ $=$ $73.209$ $73.209$

Checking:

A way to check is to list all place values and add them together

$Tens = 70$ $\text(Tens)=70$

$Units = 3$ $\text(Units)=3$

$Tenths = 0.2$ $\text(Tenths)=0.2$

$Thousandths = 0.009$ $\text(Thousandths)=0.009$

$7$ $7$ $0$ $0$ $.$ $.$ $0$ $0$ $0$ $0$ $0$ $0$

$+$ $+$ $3$ $3$ $.$ $.$ $0$ $0$ $0$ $0$ $0$ $0$

$+$ $+$ $0$ $0$ $.$ $.$ $2$ $2$ $0$ $0$ $0$ $0$

$+$ $+$ $0$ $0$ $.$ $.$ $0$ $0$ $0$ $0$ $9$ $9$

$7$ $7$ $3$ $3$ $.$ $.$ $2$ $2$ $0$ $0$ $9$ $9$

Since the answers match, the decimal form is correct.

$73.209$ $73.209$
Question 4 of 5

4. Question
Find the value of the underlined digit

$\underline{8}5.204$
- (80)
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To identify the place value of a digit, match the given value to its corresponding place value

$Place Values$ $\text(Place Values)$

Hundreds Tens Units $.$ $.$ Tenths Hundredths Thousandths

$100$ $100$ $10$ $10$ $1$ $1$ $.$ $.$ $\frac{1}{10}$ $1/10$ $\frac{1}{100}$ $1/100$ $\frac{1}{1000}$ $1/1000$

Match the given values to the corresponding place values in the table.

$\color{#00880a}{\underline8}5.204$

Tens Units $.$ $.$ Tenths Hundredths Thousandths

$10$ $10$ $1$ $1$ $.$ $.$ $\frac{1}{10}$ $1/10$ $\frac{1}{100}$ $1/100$ $\frac{1}{1000}$ $1/1000$

$8$ $8$ $5$ $5$ $.$ $.$ $2$ $2$ $0$ $0$ $4$ $4$

Next, multiply $8$ $8$ to its corresponding place value, which is tens ( $10$ $10$ ).

$8$ $8$ $\times$ $xx$ $10$ $10$ $=$ $=$ $80$ $80$

The place value of $8$ $8$ in $85.204$ $85.204$ is $80$ $80$ .

$80$ $80$
Question 5 of 5

5. Question
Find the value of the underlined digit

$2\underline{3}.125$
- (3)
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To identify the place value of a digit, match the given value to its corresponding place value

$Place Values$ $\text(Place Values)$

Hundreds Tens Units $.$ $.$ Tenths Hundredths Thousandths

$100$ $100$ $10$ $10$ $1$ $1$ $.$ $.$ $\frac{1}{10}$ $1/10$ $\frac{1}{100}$ $1/100$ $\frac{1}{1000}$ $1/1000$

Match the given values to the corresponding place values in the table.

$2\color{#00880a}{\underline3}.125$

Tens Units $.$ $.$ Tenths Hundredths Thousandths

$10$ $10$ $1$ $1$ $.$ $.$ $\frac{1}{10}$ $1/10$ $\frac{1}{100}$ $1/100$ $\frac{1}{1000}$ $1/1000$

$2$ $2$ $3$ $3$ $.$ $.$ $1$ $1$ $2$ $2$ $5$ $5$

Next, multiply $3$ $3$ to its corresponding place value, which is units ( $1$ $1$ ).

$3$ $3$ $\times$ $xx$ $1$ $1$ $=$ $=$ $3$ $3$

The place value of $3$ $3$ in $23.125$ $23.125$ is $3$ $3$ .

$3$ $3$

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Quiz summary

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1. Question

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2. Question

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3. Question

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4. Question

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5. Question

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Quizzes

Hundreds	Tens	Units	$.$ $.$	Tenths	Hundredths	Thousandths
$Place Values$ $\text(Place Values)$
$100$ $100$	$10$ $10$	$1$ $1$	$.$ $.$	$\frac{1}{10}$ $1/10$	$\frac{1}{100}$ $1/100$	$\frac{1}{1000}$ $1/1000$

	$7$ $7$	$0$ $0$	$.$ $.$	$0$ $0$	$0$ $0$	$0$ $0$
$+$ $+$		$3$ $3$	$.$ $.$	$0$ $0$	$0$ $0$	$0$ $0$
$+$ $+$		$0$ $0$	$.$ $.$	$2$ $2$	$0$ $0$	$0$ $0$
$+$ $+$		$0$ $0$	$.$ $.$	$0$ $0$	$0$ $0$	$9$ $9$
	$7$ $7$	$3$ $3$	$.$ $.$	$2$ $2$	$0$ $0$	$9$ $9$