This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions to the problems. Q19. Without using a calculator, arrange 2^3, 3^2, 5^1, 10^0 in ascending order. Show your working using powers of 10. Step 1: Calculate the value of each expression. 2^3 = 2 × 2 × 2 = 8 3^2 = 3 × 3 = 9 5^1 = 5 10^0 = 1 Step 2: Express each value using powers of 10 to show their magnitude. 10^0 = 1 5^1 = 5 2^3 = 8 3^2 = 9 All these values are greater than or equal to 10^0 and less than 10^1 (which is 10). Step 3: Arrange the original expressions in ascending order based on their calculated values. Comparing the values 1, 5, 8, 9: 1 < 5 < 8 < 9 Therefore, the expressions in ascending order are: 10^0, 5^1, 2^3, 3^2 The expressions in ascending order are 10^0, 5^1, 2^3, 3^2. Q20. Real-Life connect: Find the approximate distance from Earth to at least 3 planets in km. Express each in standard form and compare using power of 10. Step 1: Identify three planets and their approximate average distances from Earth. We will use Mars, Jupiter, and Saturn. • Approximate average distance from Earth to Mars: 225,000,000 km • Approximate average distance from Earth to Jupiter: 778,000,000 km • Approximate average distance from Earth to Saturn: 1,400,000,000 km Step 2: Express each distance in standard form (scientific notation). Standard form is written as a × 10^n, where 1 a < 10 and n is an integer. • Mars: 225,000,000 km = 2.25 × 10^8 km • Jupiter: 778,000,000 km = 7.78 × 10^8 km • Saturn: 1,400,000,000 km = 1.4 × 10^9 km Step 3: Compare the distances using powers of 10. To compare, we first look at the exponent of 10. A larger exponent means a larger number. • Saturn's distance has an exponent of 9 (10^9). • Mars' and Jupiter's distances both have an exponent of 8 (10^8). Since 10^8 < 10^9, Saturn is farther than both Mars and Jupiter. To compare Mars and Jupiter, we look at their coefficients because their powers of 10 are the same: 2.25 < 7.78. So, Mars is closer than Jupiter. Step 4: State the comparison in ascending order. The distances in ascending order are: Mars (2.25 × 10^8 km) < Jupiter (7.78 × 10^8 km) < Saturn (1.4 × 10^9 km). The approximate distances from Earth to three planets, expressed in standard form and compared, are: • Mars: 2.25 × 10^8 km • Jupiter: 7.78 × 10^8 km • Saturn: 1.4 × 10^9 km Comparison: Mars < Jupiter < Saturn. 3 done, 2 left today. You're making progress.