1. Represent each number in standard form or expanded form. 1.a) Write 349007.9 in expanded form. Expanded form means expressing the number as the sum of each digit multiplied by its place value. $$349007.9 = 300000 + 40000 + 9000 + 0 + 0 + 7 + 0.9$$ 1.b) Write "six hundred forty-two thousand thirty-one" in standard form. Standard form means writing the number as digits. Six hundred forty-two thousand thirty-one is: $$642031$$ 1.c) Write 904862 in English words. 904862 is: Nine hundred four thousand eight hundred sixty-two 1.d) Write 890431 in Chinese (中文). 890431 in Chinese is: 八十九万零四百三十一 1.e) Write the sum $500000 + 70000 + 2000 + 600 + 10 + 3 + 0.1 + 0.09$ in standard form. Add all parts: $$500000 + 70000 = 570000$$ $$570000 + 2000 = 572000$$ $$572000 + 600 = 572600$$ $$572600 + 10 = 572610$$ $$572610 + 3 = 572613$$ $$572613 + 0.1 = 572613.1$$ $$572613.1 + 0.09 = 572613.19$$ So the standard form is: $$572613.19$$ 2. Compare numbers using >, < or =. 2.a) Compare 3984 and 3948. Since 3984 is greater than 3948, we write: $$3984 > 3948$$ 2.b) Compare 68320 and 68230. $$68320 > 68230$$ 2.c) Compare 490782 and 490729. $$490782 > 490729$$ 2.d) Compare 25.36 and 25.65. $$25.36 < 25.65$$ 2.e) Compare 38.7 and 8.37. $$38.7 > 8.37$$ 3. Write the value of each underlined digit. The value of a digit depends on its place value. 3.a) In 4907, the underlined digit is 9 (hundreds place), value: $$9 \times 100 = 900$$ 3.b) In 37590.6, underlined digit is 7 (thousands place), value: $$7 \times 1000 = 7000$$ 3.c) In 159783, underlined digit is 9 (thousands place), value: $$9 \times 1000 = 9000$$ 3.d) In 8433.04, underlined digit is 3 (ones place), value: $$3 \times 1 = 3$$ 3.e) In 69405, underlined digit is 4 (hundreds place), value: $$4 \times 100 = 400$$ Part II 1. Write numbers in order from least to greatest. 1.a) Numbers: 7382.01, 8723.1, 7238.01, 7302.08, 8237.1 Order: $$7238.01 < 7302.08 < 7382.01 < 8237.1 < 8723.1$$ 1.b) Numbers: 8396.04, 8369.1, 8396.02 Order: $$8369.1 < 8396.02 < 8396.04$$ 1.c) Numbers: 84352.3, 84352.03, 8432.3 Order: $$8432.3 < 84352.03 < 84352.3$$ 1.d) Numbers: 10903, 19003, 10930, 1903 Order: $$1903 < 10903 < 10930 < 19003$$ 2. Rounding numbers. 2.a) Round 90234 to nearest hundred. Look at tens digit (3), less than 5, round down: $$90200$$ 2.b) Round 35872 to nearest thousand. Look at hundreds digit (8), 5 or more, round up: $$36000$$ 2.c) Round 3.25 to nearest tenth. Look at hundredths digit (5), 5 or more, round up: $$3.3$$ 2.d) Round 84.74 to nearest whole number. Look at tenths digit (7), 5 or more, round up: $$85$$ 3. Complete the number sequence and explain the pattern. 3.a) Sequence: 16, __, 48, 64, __ Pattern: Multiply by 1.5 then by 1.333... Calculate missing terms: Second term: $$16 \times 1.5 = 24$$ Fifth term: $$64 \times 1.5 = 96$$ Sequence: 16, 24, 48, 64, 96 Pattern rule: Multiply by alternating factors 1.5 and 1.333... 3.b) Sequence: __, 900, 850, __, 750 Pattern: Decrease by 50 each step. First term: $$900 + 50 = 950$$ Fourth term: $$850 - 50 = 800$$ Sequence: 950, 900, 850, 800, 750 Pattern rule: Subtract 50 each time. 3.c) Sequence: 256, __, __, 4, 1 Pattern: Divide by 4 each step. Second term: $$256 \div 4 = 64$$ Third term: $$64 \div 4 = 16$$ Sequence: 256, 64, 16, 4, 1 Pattern rule: Divide by 4 each time. 3.d) Sequence: 6, __, 150, __, 3750 Pattern: Multiply by 5 each step. Second term: $$6 \times 5 = 30$$ Fourth term: $$150 \times 5 = 750$$ Sequence: 6, 30, 150, 750, 3750 Pattern rule: Multiply by 5 each time. 4. Write down the total amount of money shown below. (No image provided, so cannot answer.) Part III 1. Draw three different coin combinations to represent 13.70. One combination should use the fewest coins possible. Example combinations: - Fewest coins: 1 ten-dollar bill, 3 one-dollar coins, 2 quarters, 2 dimes - Another: 13 one-dollar coins, 2 quarters, 2 dimes - Another: 10 one-dollar coins, 7 quarters, 2 dimes Final answer summary: 1.a) Expanded form: $$300000 + 40000 + 9000 + 0 + 0 + 7 + 0.9$$ 1.b) Standard form: $$642031$$ 1.c) English: Nine hundred four thousand eight hundred sixty-two 1.d) 中文: 八十九万零四百三十一 1.e) Standard form: $$572613.19$$ 2.a) $$3984 > 3948$$ 2.b) $$68320 > 68230$$ 2.c) $$490782 > 490729$$ 2.d) $$25.36 < 25.65$$ 2.e) $$38.7 > 8.37$$ 3.a) $$900$$ 3.b) $$7000$$ 3.c) $$9000$$ 3.d) $$3$$ 3.e) $$400$$ II.1.a) $$7238.01 < 7302.08 < 7382.01 < 8237.1 < 8723.1$$ II.1.b) $$8369.1 < 8396.02 < 8396.04$$ II.1.c) $$8432.3 < 84352.03 < 84352.3$$ II.1.d) $$1903 < 10903 < 10930 < 19003$$ II.2.a) $$90200$$ II.2.b) $$36000$$ II.2.c) $$3.3$$ II.2.d) $$85$$ II.3.a) 16, 24, 48, 64, 96; multiply by 1.5 then 1.333... II.3.b) 950, 900, 850, 800, 750; subtract 50 each time II.3.c) 256, 64, 16, 4, 1; divide by 4 each time II.3.d) 6, 30, 150, 750, 3750; multiply by 5 each time III.1) Examples of coin combinations for 13.70 given above.