Write the following numbers in scientific notation
A.1001
B. 53
C. 6,926,300,000
D .-392
E. 0.00361
The correct answer and explanation is :
Let’s write each of the following numbers in scientific notation, and I’ll explain the process of converting them:
A. 1001
Scientific notation expresses a number as a product of two factors:
- A number between 1 and 10.
- A power of 10.
For 1001, we want to rewrite it as a number between 1 and 10, so we move the decimal point to the left by 3 places (1001 becomes 1.001). Since we moved the decimal 3 places, the exponent for the power of 10 will be 3.
Answer:
1001 = $1.001 \times 10^3$
B. 53
For 53, we move the decimal point two places to the left, turning 53 into 5.3. Since we moved the decimal two places, the exponent for the power of 10 will be 2.
Answer:
53 = $5.3 \times 10^1$
C. 6,926,300,000
This large number is written in scientific notation by moving the decimal point to the left until it falls between 6 and 7. We move the decimal 9 places, so the exponent of 10 will be 9.
Answer:
6,926,300,000 = $6.9263 \times 10^9$
D. -392
For negative numbers, the process is the same as for positive numbers, except the number will have a negative sign. We move the decimal point two places to the left (turning -392 into -3.92), so the exponent will be 2.
Answer:
-392 = $-3.92 \times 10^2$
E. 0.00361
For numbers less than 1, we move the decimal point to the right. For 0.00361, we move the decimal point 3 places to the right, turning it into 3.61. Since we moved the decimal to the right, the exponent will be negative, -3.
Answer:
0.00361 = $3.61 \times 10^{-3}$
Explanation:
Scientific notation is a way of simplifying large or small numbers, making them easier to work with. The general form is:
$$
a \times 10^n
$$
where $a$ is a number greater than or equal to 1 but less than 10, and $n$ is an integer representing the power of 10 that shifts the decimal point. For large numbers, $n$ is positive, and for small numbers, $n$ is negative. The exponent indicates how many places the decimal point has been moved. This system is especially useful in scientific calculations, where precision and simplicity are necessary.