Question

1. write a symbol (<, >, =) in each circle to compare the two numbers. a) 3.2 × 10⁻² ◯ 3.2 × 10⁻³ b) 6.7 × 10² ◯ 7.6 × 10² c) 2.9 × 10⁰ ◯ 1.1 × 10¹

Explanation:

Part A

Step1: Recall negative exponent rule

For \(a\times10^{-n}\), as \(n\) increases, the number gets smaller. Here, compare exponents: \(-2\) vs \(-3\). Since \(-2 > -3\), \(10^{-2}>10^{-3}\).

Step2: Compare the numbers

Both have coefficient \(3.2\), so \(3.2\times10^{-2}>3.2\times10^{-3}\).

Part B

Step1: Observe the powers of 10

Both have \(10^{2}\), so compare coefficients \(6.7\) and \(7.6\).

Step2: Compare coefficients

Since \(6.7 < 7.6\), \(6.7\times10^{2}<7.6\times10^{2}\).

Part C

Step1: Simplify the numbers

\(10^{0} = 1\), so \(2.9\times10^{0}=2.9\). \(10^{1}=10\), so \(1.1\times10^{1}=11\).

Step2: Compare the simplified numbers

Since \(2.9 < 11\), \(2.9\times10^{0}<1.1\times10^{1}\).

Answer:

A) \(>\)
B) \(<\)
C) \(<\)