Question

Put in scientific notation: 417291 * 10^5, 1.432 * 10x^-4

Answer 1

Put in regular notation: 1.42 x 10^5, 4.85 x 10^-4

Answer 2

Correct these: .15 x 10^3, 20 x 10^-2

Answer 3

Let’s look at Rylee(dog). Which weight is most accurate?

A) 15 lbs
B) 15.0 lbs
C) 15.09 lbs

Answer 4

To express the numbers in proper scientific notation:

1. For \( 417291 \times 10^5 \):
- First, we need to express \( 417291 \) in scientific notation. We can write it as \( 4.17291 \times 10^5 \).
- Combining that with \( 10^5 \):
\[
4.17291 \times 10^5 \times 10^5 = 4.17291 \times 10^{10}
\]

2. For \( 1.432 \times 10^{-4} \):
- This is already in scientific notation, so it remains as:
\[
1.432 \times 10^{-4}
\]

Thus, the numbers in scientific notation are:
- \( 4.17291 \times 10^{10} \)
- \( 1.432 \times 10^{-4} \)

Answer 5

To convert the numbers from scientific notation to regular notation:

1. For \( 1.42 \times 10^5 \):

\[
1.42 \times 10^5 = 1.42 \times 100000 = 142000
\]

So, \( 1.42 \times 10^5 = 142000 \).

2. For \( 4.85 \times 10^{-4} \):

\[
4.85 \times 10^{-4} = 4.85 \times 0.0001 = 0.000485
\]

So, \( 4.85 \times 10^{-4} = 0.000485 \).

In regular notation, the numbers are:
- \( 1.42 \times 10^5 = 142000 \)
- \( 4.85 \times 10^{-4} = 0.000485 \)

Answer 6

To express the numbers in proper scientific notation, we need to ensure that the coefficient is between 1 and 10.

1. For \( 0.15 \times 10^3 \):
- First, we rewrite \( 0.15 \) in scientific notation:
\[
0.15 = 1.5 \times 10^{-1}
\]
- Now, combine this with \( 10^3 \):
\[
(1.5 \times 10^{-1}) \times 10^3 = 1.5 \times 10^{2}
\]

2. For \( 20 \times 10^{-2} \):
- Rewrite \( 20 \) in scientific notation:
\[
20 = 2.0 \times 10^{1}
\]
- Now, combine this with \( 10^{-2} \):
\[
(2.0 \times 10^{1}) \times 10^{-2} = 2.0 \times 10^{-1}
\]

So the corrected scientific notations are:
- \( 0.15 \times 10^3 = 1.5 \times 10^2 \)
- \( 20 \times 10^{-2} = 2.0 \times 10^{-1} \)

Answer 7

In terms of precision in reporting weight, the most accurate measurement would be the one that conveys the greatest detail about the value.

Here’s a breakdown of the options:

A) **15 lbs** - This measurement does not indicate any decimal places, so it suggests a rounding to the nearest whole pound.

B) **15.0 lbs** - This measurement implies a precision to one decimal place, indicating that the weight is measured with a degree of accuracy to the nearest tenth of a pound.

C) **15.09 lbs** - This measurement indicates precision to the hundredths place, suggesting that the weight is measured with even greater accuracy.

Based on this analysis, **C) 15.09 lbs** is the most accurate measurement because it provides the greatest level of detail with respect to the dog's weight.