How many times is 4 times 10^4 larger than 2 times 10^2?

Answer 1

To determine how many times \(4 \times 10^4\) is larger than \(2 \times 10^2\), we can set up the expression:

\[ \text{Factor} = \frac{4 \times 10^4}{2 \times 10^2} \]

Now, we simplify the expression step by step.

1. Divide the coefficients: \[ \frac{4}{2} = 2 \]

2. Divide the powers of ten: \[ \frac{10^4}{10^2} = 10^{4-2} = 10^2 \]

3. Combine the results: \[ \text{Factor} = 2 \times 10^2 \]

Now, we can evaluate \(2 \times 10^2\): \[ 2 \times 10^2 = 2 \times 100 = 200 \]

Thus, \(4 \times 10^4\) is 200 times larger than \(2 \times 10^2\).

The final answer is: \[ \boxed{200} \]

Answer 2

At the end of fiscal year 2004, the federal dept Country C is $278,560 125,000. What is the closest ESTIMATION of this amount? Express your answer in the form of a single digit times an integer power of 10.

Answer 3

To estimate the federal debt of Country C, which is given as \( 278,560,125,000 \), we can simplify the number by rounding it to the nearest significant digit.

1. Identify the leading digit: The leading digit is \( 2 \).

2. Estimate the rest in terms of powers of ten:

   • The number \( 278,560,125,000 \) can be approximated to \( 280,000,000,000 \) for estimation purposes.

3. Express this in scientific notation:

   • \( 280,000,000,000 \) can be written as \( 2.8 \times 10^{11} \).

Therefore, the closest estimation of the federal debt of Country C, expressed in the form of a single digit times an integer power of 10, is:

\[ \boxed{2.8 \times 10^{11}} \]

Answer 4

the first number is supposed to be single digit.

Answer 5

Apologies for the oversight. You are correct that the first number should be a single digit. Let's re-evaluate the approximation of \( 278,560,125,000 \).

1. Identify the significant figures: The number \( 278,560,125,000 \) starts with the digit \( 2 \).
2. Round it to a single digit: We can round \( 278,560,125,000 \) to \( 3 \times 10^{11} \) because the first significant figure in the rounding is \( 3 \).

Here’s how it breaks down:

• \( 278,560,125,000 \) is closer to \( 300,000,000,000 \), which can be rounded as:

\[ 3 \times 10^{11} \]

So, the closest estimation of \( 278,560,125,000 \) in the required form of a single digit times an integer power of 10 is:

\[ \boxed{3 \times 10^{11}} \]

Answer 6

How many times less is 10^2 than 10^6? Express your answer as an integer power of 10.

10^4
10^-4
0.0001
10,000

Answer 7

To determine how many times less \(10^2\) is than \(10^6\), we can set up the following calculation:

\[ \frac{10^6}{10^2} \]

Using the properties of exponents, specifically \( \frac{a^m}{a^n} = a^{m-n} \), we can simplify this expression:

\[ \frac{10^6}{10^2} = 10^{6-2} = 10^4 \]

This means that \(10^2\) is \(10^4\) times less than \(10^6\).

Thus, the expression for how many times less \(10^2\) is than \(10^6\) can be expressed as:

\[ \boxed{10^{-4}} \]

This indicates that \(10^2\) is \(10^{-4}\) times in relation to \(10^6\). However, it's more common to state the increase in terms of \(10^4\) instead. Thus, the clear understanding is that \(10^2\) is \(10^4\) times less than \(10^6\).

So, the final answer that best fits your original question regarding how many times less is \(10^2\) compared to \(10^6\) is:

\[ \boxed{10^{-4}} \]

Answer 8

Roughly, it takes light less than 0.000000003 of a second to travel a one-meter distance. Express this number in the form of A times 10^n where 1<A<10 and is a one-digit number.

Answer 9

To express \(0.000000003\) in the form of \(A \times 10^n\), where \(1 < A < 10\), we first need to rewrite the number in scientific notation.

1. Write the number in decimal form: \[ 0.000000003 \]

2. Move the decimal point to the right to obtain a number between \(1\) and \(10\). We move the decimal point \(9\) places to the right: \[ 3.0 \]

3. Express this as a power of ten: \[ 3.0 = 3.0 \times 10^{-9} \]

Thus, we can express \(0.000000003\) as:

\[ \boxed{3 \times 10^{-9}} \]

This is in the required format \(A \times 10^n\) where \(1 < A < 10\).