Subtract numbers in scientific notation practice
Sure! Here are a few examples for you to practice subtracting numbers in scientific notation:
Example 1:
(5.4 x 10^7) - (3.2 x 10^6) =
To subtract these numbers, we need to ensure that the exponents are the same. In this case, we can rewrite 3.2 x 10^6 as 0.32 x 10^7 (since moving the decimal one place to the left increases the exponent by 1).
Now we can subtract the mantissas (the numbers before the exponent):
5.4 - 0.32 = 5.08
Finally, we keep the common exponent:
5.08 x 10^7
Example 2:
(6.75 x 10^4) - (1.25 x 10^3) =
Again, we need to ensure that the exponents are the same. We can rewrite 1.25 x 10^3 as 0.125 x 10^4.
Subtract the mantissas:
6.75 - 0.125 = 6.625
Keep the common exponent:
6.625 x 10^4
Example 3:
(9.12 x 10^8) - (2.5 x 10^7) =
The exponents are already the same, so no need for any adjustments.
Subtract the mantissas:
9.12 - 2.5 = 6.62
Keep the common exponent:
6.62 x 10^8
I hope this helps! Let me know if you have any more questions.
To subtract numbers in scientific notation, follow these steps:
Step 1: Ensure that the exponents are the same for both numbers.
If the exponents are already the same, move to step 2. Otherwise, you need to adjust the exponents. To do this, use the following steps:
a) Determine the difference between the two exponents.
b) Shift the decimal point of the number with the smaller exponent to the right by the same number of places as the difference in exponents.
c) Adjust the exponent of the number accordingly.
Step 2: Subtract the coefficients.
Simply subtract the coefficients of the numbers, while keeping the common exponent unchanged.
Step 3: Express the result in scientific notation.
If necessary, adjust the decimal point and the exponent to express the result in scientific notation.
Here's an example to illustrate the steps:
Example:
Subtract 2.45 × 10^5 from 8.72 × 10^4.
Step 1: Adjust the exponents.
Since the exponents are already the same, we can move to step 2.
Step 2: Subtract the coefficients.
8.72 - 2.45 = 6.27
Step 3: Express the result in scientific notation.
The result is 6.27 × 10^4.
Therefore, 8.72 × 10^4 - 2.45 × 10^5 = 6.27 × 10^4.
Sure! Subtracting numbers in scientific notation involves subtracting the coefficients (the numbers before the "x10") and keeping the same exponent.
Here's a step-by-step example to help you practice:
Question: Subtract (3.8 x 10^4) - (1.2 x 10^3)
Step 1: First, let's subtract the coefficients: 3.8 - 1.2 = 2.6
Step 2: Next, we keep the exponent the same. In this case, both numbers have an exponent of 10^4.
Step 3: Put the final answer in scientific notation format: 2.6 x 10^4
So, the answer to (3.8 x 10^4) - (1.2 x 10^3) is 2.6 x 10^4.
Remember to always pay attention to both the coefficients and the exponents when subtracting numbers in scientific notation.