Math / Numbers & Operations

QuestionFay thinks that one billion is the same as $10^{2} \times 10^{7}$ Joe thinks that one billion is the same a $10^{3} \times 10^{6}$ Explain why they are both correct.

Studdy Solution

STEP 1

1. We need to verify the equivalence of $10^{2} \times 10^{7}$ and $10^{3} \times 10^{6}$ to one billion.
2. One billion is equal to $10^{9}$ .

STEP 2

1. Verify Fay's expression.
2. Verify Joe's expression.
3. Conclude both expressions are equivalent to one billion.

STEP 3

Verify Fay's expression: $10^{2} \times 10^{7}$ .
$10^{2} \times 10^{7} = 10^{2 + 7} = 10^{9}$

STEP 4

Verify Joe's expression: $10^{3} \times 10^{6}$ .
$10^{3} \times 10^{6} = 10^{3 + 6} = 10^{9}$

STEP 5

Since both expressions simplify to $10^{9}$ , they both represent one billion.
Both Fay and Joe are correct because their expressions simplify to:
$\boxed{10^{9}}$

Was this helpful?

QuestionFay thinks that one billion is the same as $10^{2} \times 10^{7}$ Joe thinks that one billion is the same a $10^{3} \times 10^{6}$ Explain why they are both correct.

Studdy Solution

STEP 1

1. We need to verify the equivalence of $10^{2} \times 10^{7}$ and $10^{3} \times 10^{6}$ to one billion.
2. One billion is equal to $10^{9}$ .

STEP 2

1. Verify Fay's expression.
2. Verify Joe's expression.
3. Conclude both expressions are equivalent to one billion.

STEP 3

Verify Fay's expression: $10^{2} \times 10^{7}$ .
$10^{2} \times 10^{7} = 10^{2 + 7} = 10^{9}$

STEP 4

Verify Joe's expression: $10^{3} \times 10^{6}$ .
$10^{3} \times 10^{6} = 10^{3 + 6} = 10^{9}$

STEP 5

Since both expressions simplify to $10^{9}$ , they both represent one billion.
Both Fay and Joe are correct because their expressions simplify to:
$\boxed{10^{9}}$

Get Studdy

Studdy solves anything!

Start learning now

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

QuestionFay thinks that one billion is the same as 102×10710^{2} \times 10^{7}102×107 Joe thinks that one billion is the same a 103×10610^{3} \times 10^{6}103×106 Explain why they are both correct.

Studdy Solution

STEP 1

1. We need to verify the equivalence of 102×10710^{2} \times 10^{7}102×107 and 103×10610^{3} \times 10^{6}103×106 to one billion.2. One billion is equal to 10910^{9}109.

STEP 2

1. Verify Fay's expression.2. Verify Joe's expression.3. Conclude both expressions are equivalent to one billion.

STEP 3

Verify Fay's expression: 102×10710^{2} \times 10^{7}102×107.102×107=102+7=10910^{2} \times 10^{7} = 10^{2 + 7} = 10^{9}102×107=102+7=109

STEP 4

Verify Joe's expression: 103×10610^{3} \times 10^{6}103×106.103×106=103+6=10910^{3} \times 10^{6} = 10^{3 + 6} = 10^{9}103×106=103+6=109

STEP 5

Since both expressions simplify to 10910^{9}109, they both represent one billion. Both Fay and Joe are correct because their expressions simplify to:109\boxed{10^{9}}109​

Get Studdy

Studdy solves anything!

Start learning now

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

QuestionFay thinks that one billion is the same as $10^{2} \times 10^{7}$ Joe thinks that one billion is the same a $10^{3} \times 10^{6}$ Explain why they are both correct.

1. We need to verify the equivalence of $10^{2} \times 10^{7}$ and $10^{3} \times 10^{6}$ to one billion.
2. One billion is equal to $10^{9}$ .

1. Verify Fay's expression.
2. Verify Joe's expression.
3. Conclude both expressions are equivalent to one billion.

Verify Fay's expression: $10^{2} \times 10^{7}$ .
$10^{2} \times 10^{7} = 10^{2 + 7} = 10^{9}$

Verify Joe's expression: $10^{3} \times 10^{6}$ .
$10^{3} \times 10^{6} = 10^{3 + 6} = 10^{9}$

Since both expressions simplify to $10^{9}$ , they both represent one billion.
Both Fay and Joe are correct because their expressions simplify to:
$\boxed{10^{9}}$