Math / Numbers & Operations

Question $\frac{3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}}{1.5 \times 10^{15} \mathrm{~Hz}}$

Studdy Solution

STEP 1

1. We are given a division problem involving scientific notation.
2. The numerator is $3.00 \times 10^{8} \, \text{m/s}$ .
3. The denominator is $1.5 \times 10^{15} \, \text{Hz}$ .
4. We need to simplify the expression.

STEP 2

1. Divide the coefficients.
2. Subtract the exponents.
3. Write the final expression in scientific notation.

STEP 3

Divide the coefficients of the numbers in scientific notation.
$\frac{3.00}{1.5} = 2.00$

STEP 4

Subtract the exponents in the powers of ten.
$10^{8} \div 10^{15} = 10^{8 - 15} = 10^{-7}$

STEP 5

Combine the results from Step 1 and Step 2 to write the final expression in scientific notation.
$2.00 \times 10^{-7}$
The simplified expression is:
$\boxed{2.00 \times 10^{-7} \, \text{m} \cdot \text{s}}$

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Question $\frac{3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}}{1.5 \times 10^{15} \mathrm{~Hz}}$

Studdy Solution

STEP 1

1. We are given a division problem involving scientific notation.
2. The numerator is $3.00 \times 10^{8} \, \text{m/s}$ .
3. The denominator is $1.5 \times 10^{15} \, \text{Hz}$ .
4. We need to simplify the expression.

STEP 2

1. Divide the coefficients.
2. Subtract the exponents.
3. Write the final expression in scientific notation.

STEP 3

Divide the coefficients of the numbers in scientific notation.
$\frac{3.00}{1.5} = 2.00$

STEP 4

Subtract the exponents in the powers of ten.
$10^{8} \div 10^{15} = 10^{8 - 15} = 10^{-7}$

STEP 5

Combine the results from Step 1 and Step 2 to write the final expression in scientific notation.
$2.00 \times 10^{-7}$
The simplified expression is:
$\boxed{2.00 \times 10^{-7} \, \text{m} \cdot \text{s}}$

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Question3.00×108 m/s1.5×1015 Hz\frac{3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}}{1.5 \times 10^{15} \mathrm{~Hz}}1.5×1015 Hz3.00×108 m/s​

Studdy Solution

STEP 1

1. We are given a division problem involving scientific notation.2. The numerator is 3.00×108 m/s 3.00 \times 10^{8} \, \text{m/s} 3.00×108m/s.3. The denominator is 1.5×1015 Hz 1.5 \times 10^{15} \, \text{Hz} 1.5×1015Hz.4. We need to simplify the expression.

STEP 2

1. Divide the coefficients.2. Subtract the exponents.3. Write the final expression in scientific notation.

STEP 3

Divide the coefficients of the numbers in scientific notation.3.001.5=2.00 \frac{3.00}{1.5} = 2.00 1.53.00​=2.00

STEP 4

Subtract the exponents in the powers of ten.108÷1015=108−15=10−7 10^{8} \div 10^{15} = 10^{8 - 15} = 10^{-7} 108÷1015=108−15=10−7

STEP 5

Combine the results from Step 1 and Step 2 to write the final expression in scientific notation.2.00×10−7 2.00 \times 10^{-7} 2.00×10−7 The simplified expression is:2.00×10−7 m⋅s\boxed{2.00 \times 10^{-7} \, \text{m} \cdot \text{s}}2.00×10−7m⋅s​

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Question $\frac{3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}}{1.5 \times 10^{15} \mathrm{~Hz}}$

1. We are given a division problem involving scientific notation.
2. The numerator is $3.00 \times 10^{8} \, \text{m/s}$ .
3. The denominator is $1.5 \times 10^{15} \, \text{Hz}$ .
4. We need to simplify the expression.

1. Divide the coefficients.
2. Subtract the exponents.
3. Write the final expression in scientific notation.

Divide the coefficients of the numbers in scientific notation.
$\frac{3.00}{1.5} = 2.00$

Subtract the exponents in the powers of ten.
$10^{8} \div 10^{15} = 10^{8 - 15} = 10^{-7}$

Combine the results from Step 1 and Step 2 to write the final expression in scientific notation.
$2.00 \times 10^{-7}$
The simplified expression is:
$\boxed{2.00 \times 10^{-7} \, \text{m} \cdot \text{s}}$