Solved on Jan 22, 2024

Find the products of $0.009 \times 10$ , $3.1 \times 10^{3}$ , $0.062 \times 10^{2}$ , and $1.24 \times 10^{4}$ .

STEP 1

Assumptions
1. We are multiplying decimal numbers by powers of 10.
2. The multiplication of a decimal number by a power of 10 shifts the decimal point to the right by the number of zeros in the power of 10.

STEP 2

For problem 2, multiply $0.009$ by $10$ .
$0.009 \times 10$

STEP 3

Since multiplying by 10 is equivalent to shifting the decimal point one place to the right, we get:
$0.009 \times 10 = 0.09$

STEP 4

For problem 3, multiply $3.1$ by $10^{3}$ .
$3.1 \times 10^{3}$

STEP 5

Multiplying by $10^{3}$ (which is $1000$ ) shifts the decimal point three places to the right, so we get:
$3.1 \times 10^{3} = 3100$

STEP 6

For problem 4, multiply $0.062$ by $10^{2}$ .
$0.062 \times 10^{2}$

STEP 7

Multiplying by $10^{2}$ (which is $100$ ) shifts the decimal point two places to the right, giving us:
$0.062 \times 10^{2} = 6.2$

STEP 8

For problem 5, multiply $1.24$ by $10^{4}$ .
$1.24 \times 10^{4}$

STEP 9

Multiplying by $10^{4}$ (which is $10000$ ) shifts the decimal point four places to the right, resulting in:
$1.24 \times 10^{4} = 12400$
The products for the given problems are:
2. $0.09$
3. $3100$
4. $6.2$
5. $12400$

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Find the products of $0.009 \times 10$ , $3.1 \times 10^{3}$ , $0.062 \times 10^{2}$ , and $1.24 \times 10^{4}$ .

STEP 1

Assumptions
1. We are multiplying decimal numbers by powers of 10.
2. The multiplication of a decimal number by a power of 10 shifts the decimal point to the right by the number of zeros in the power of 10.

STEP 2

For problem 2, multiply $0.009$ by $10$ .
$0.009 \times 10$

STEP 3

Since multiplying by 10 is equivalent to shifting the decimal point one place to the right, we get:
$0.009 \times 10 = 0.09$

STEP 4

For problem 3, multiply $3.1$ by $10^{3}$ .
$3.1 \times 10^{3}$

STEP 5

Multiplying by $10^{3}$ (which is $1000$ ) shifts the decimal point three places to the right, so we get:
$3.1 \times 10^{3} = 3100$

STEP 6

For problem 4, multiply $0.062$ by $10^{2}$ .
$0.062 \times 10^{2}$

STEP 7

Multiplying by $10^{2}$ (which is $100$ ) shifts the decimal point two places to the right, giving us:
$0.062 \times 10^{2} = 6.2$

STEP 8

For problem 5, multiply $1.24$ by $10^{4}$ .
$1.24 \times 10^{4}$

STEP 9

Multiplying by $10^{4}$ (which is $10000$ ) shifts the decimal point four places to the right, resulting in:
$1.24 \times 10^{4} = 12400$
The products for the given problems are:
2. $0.09$
3. $3100$
4. $6.2$
5. $12400$

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Find the products of 0.009×100.009 \times 100.009×10, 3.1×1033.1 \times 10^{3}3.1×103, 0.062×1020.062 \times 10^{2}0.062×102, and 1.24×1041.24 \times 10^{4}1.24×104.

STEP 1

Assumptions1. We are multiplying decimal numbers by powers of 10.2. The multiplication of a decimal number by a power of 10 shifts the decimal point to the right by the number of zeros in the power of 10.

STEP 2

For problem 2, multiply 0.0090.0090.009 by 101010.0.009×100.009 \times 100.009×10

STEP 3

Since multiplying by 10 is equivalent to shifting the decimal point one place to the right, we get:0.009×10=0.090.009 \times 10 = 0.090.009×10=0.09

STEP 4

For problem 3, multiply 3.13.13.1 by 10310^{3}103.3.1×1033.1 \times 10^{3}3.1×103

STEP 5

Multiplying by 10310^{3}103 (which is 100010001000) shifts the decimal point three places to the right, so we get:3.1×103=31003.1 \times 10^{3} = 31003.1×103=3100

STEP 6

For problem 4, multiply 0.0620.0620.062 by 10210^{2}102.0.062×1020.062 \times 10^{2}0.062×102

STEP 7

Multiplying by 10210^{2}102 (which is 100100100) shifts the decimal point two places to the right, giving us:0.062×102=6.20.062 \times 10^{2} = 6.20.062×102=6.2

STEP 8

For problem 5, multiply 1.241.241.24 by 10410^{4}104.1.24×1041.24 \times 10^{4}1.24×104

STEP 9

Multiplying by 10410^{4}104 (which is 100001000010000) shifts the decimal point four places to the right, resulting in:1.24×104=124001.24 \times 10^{4} = 124001.24×104=12400The products for the given problems are:2. 0.090.090.093. 3100310031004. 6.26.26.25. 124001240012400

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the products of $0.009 \times 10$ , $3.1 \times 10^{3}$ , $0.062 \times 10^{2}$ , and $1.24 \times 10^{4}$ .

Assumptions
1. We are multiplying decimal numbers by powers of 10.
2. The multiplication of a decimal number by a power of 10 shifts the decimal point to the right by the number of zeros in the power of 10.

For problem 2, multiply $0.009$ by $10$ .
$0.009 \times 10$

Since multiplying by 10 is equivalent to shifting the decimal point one place to the right, we get:
$0.009 \times 10 = 0.09$

For problem 3, multiply $3.1$ by $10^{3}$ .
$3.1 \times 10^{3}$

Multiplying by $10^{3}$ (which is $1000$ ) shifts the decimal point three places to the right, so we get:
$3.1 \times 10^{3} = 3100$

For problem 4, multiply $0.062$ by $10^{2}$ .
$0.062 \times 10^{2}$

Multiplying by $10^{2}$ (which is $100$ ) shifts the decimal point two places to the right, giving us:
$0.062 \times 10^{2} = 6.2$

For problem 5, multiply $1.24$ by $10^{4}$ .
$1.24 \times 10^{4}$

Multiplying by $10^{4}$ (which is $10000$ ) shifts the decimal point four places to the right, resulting in:
$1.24 \times 10^{4} = 12400$
The products for the given problems are:
2. $0.09$
3. $3100$
4. $6.2$
5. $12400$