Question

50 POINTS!! Drag each label to the correct location on the image. Not all labels will be used. The values of a, b, and c in scientific notation are 3.47 × 10-6, 4.61 × 107, and 5.52 × 107, respectively. Complete the following sentences. Round so the first factor goes to the hundredths place. a*b a/b c/a 1.60 16.0 × 101 1.60 × 102 1.59 × 1013 0.75 × 10-13 7.53 × 10-13 7.53 × 10-14 1.59 × 101

Answer 1

Answer:

$\boxed{a*b = 1.60 * 10^2}$

$\boxed{a/b = 7.53 * 10^{-14}}$

$\boxed{c/a = 1.59 * 10^{13}}$

Step-by-step explanation:

a = $3.47 * 10^{-6}$

b = $4.61 * 10^7$

c = $5.52*10^7$

Finding a*b:

a*b =( $3.47 * 10^{-6}$ )*( $4.61 * 10^7$)

= (3.47*4.61) * ($10^{-6}*10^7$)

When bases are same, powers are to be added

= 15.997 * $10^{-6+7}$

= 15.997 * $10^1$

= 159.97

Rounding it off

=> 1.60 * 10²

Finding a/b:

=> $\frac{3.47*10^{-6}}{4.61*10^7}$

Using rule of exponents $a^m/a^n = a^{m-n}$

=> 0.753 * $10^{-6-7}$

=> $7.53*10^{-1}*10^{-13}$

=> $7.53 * 10^{-1-13}$

=> 7.53 * 10⁻¹⁴

Finding c/a:

=> $\frac{5.52 * 10^7}{3.47*10^{-6}}$

=> 1.59 * $10^{7+6}$

=> 1.59 * 10¹³

Answer 2

Answer:

a × b = 1.60 × 10^2

a/b = 7.52 × 10^-14

c/a = 1.59 × 10^13

Step-by-step explanation:

a = 3.47 × 10^-6

b = 4.61 × 10^7

c = 5.52 × 10^7

Solve a × b

(3.47 × 10^-6) × (4.61 × 10^7)

When bases are same in multiplication, we add the exponents.

15.9967 × 10^1

Decimal point is after first non-zero digit. Round to hundredths.

1.60 × 10^2

Solve a/b

(3.47 × 10^-6)/(4.61 × 10^7)

When bases are same in division, subtract the exponents.

3.47/4.61 × 10^-14

0.75271149674 × 10^-14

Decimal point is after first non-zero digit. Round to hundredths.

7.52 × 10^-14

Solve c/a

(5.52 × 10^7)/(3.47 × 10^-6)

When bases are same in division, subtract the exponents.

5.52/3.47 × 10^13

1.59077809798 × 10^13

Round to hundredths.

1.59 × 10^13