Question

Subtract numbers in scientific notation

Answer 1

To subtract numbers in scientific notation, you first need to ensure that the numbers have the same exponent. Here’s a step-by-step guide on how to do this:

### Step 1: Write the Numbers in Scientific Notation
For example, let's say you want to subtract \( 4.5 \times 10^6 \) from \( 2.1 \times 10^7 \).

### Step 2: Adjust the Exponents
Make sure both numbers have the same exponent. In this case, we can convert \( 2.1 \times 10^7 \) to the same exponent as \( 4.5 \times 10^6 \):

\[
2.1 \times 10^7 = 21.0 \times 10^6
\]

### Step 3: Perform the Subtraction
Now that both numbers have the same exponent, you can subtract them:

\[
21.0 \times 10^6 - 4.5 \times 10^6 = (21.0 - 4.5) \times 10^6 = 16.5 \times 10^6
\]

### Step 4: Simplify (if necessary)
Finally, you can express it in standard scientific notation form. In this case, \( 16.5 \times 10^6 \) is already in scientific notation.

### Final Answer
Thus,

\[
2.1 \times 10^7 - 4.5 \times 10^6 = 16.5 \times 10^6
\]

### Example
Let’s do another example:

**Subtract** \( 3.2 \times 10^5 \) from \( 1.5 \times 10^6 \).

1. Write down the numbers:
\[
1.5 \times 10^6, \quad 3.2 \times 10^5
\]

2. Adjust the exponent of \( 1.5 \times 10^6 \):
\[
3.2 \times 10^5 = 0.32 \times 10^6
\]

3. Now perform the subtraction:
\[
1.5 \times 10^6 - 0.32 \times 10^6 = (1.5 - 0.32) \times 10^6 = 1.18 \times 10^6
\]

### Final Answer
So,

\[
1.5 \times 10^6 - 3.2 \times 10^5 = 1.18 \times 10^6
\]

This method can be applied to any subtraction problem involving numbers in scientific notation.