Question

1. write 560, 000, 000 in scientific notation. $5.6 \cdot 10^8$ $56 \cdot 10^7$ $5.6 \cdot 10^7$ $0.56 \cdot 10^9$

Explanation:

Step1: Recall scientific notation rules

Scientific notation is in the form \( a \times 10^n \), where \( 1 \leq |a| < 10 \) and \( n \) is an integer.

Step2: Convert 560,000,000 to scientific notation

Move the decimal point to the left until there is one non - zero digit to the left of the decimal point. For 560,000,000, we move the decimal point 8 places to the left to get \( 5.6 \). The number of places we moved the decimal point is the exponent of 10. So \( 560,000,000=5.6\times10^{8} \).
Let's check the other options:

• For \( 56\times 10^{7} \), \( a = 56 \) which is not in the range \( 1\leq|a|<10 \).
• For \( 5.6\times10^{7} \), \( 5.6\times10^{7}=56,000,000

eq560,000,000 \).

• For \( 0.56\times10^{9} \), \( a = 0.56 \) is in the range, but \( 0.56\times10^{9}=560,000,000 \) is the same number, but the standard form requires \( 1\leq|a|<10 \), and \( 5.6\times10^{8} \) is a more standard form as \( 5.6 \) is in the correct range and the exponent is calculated correctly from the original number.

Answer:

A. \( 5.6\cdot10^{8} \)