📘 Quiz

Solution: Step 1: Count the number of decimal places in the first number, 95.75. It has 2 decimal places. Step 2: Count the number of decimal places in the second number, 0.02554. It has 5 decimal places. Step 3: Sum the number of decimal places: 2 + 5 = 7. Step 4: The product of 95.75 and 0.02554 will initially have 7 decimal places. Step 5: Consider the last digit of the product. The last digits of the original numbers are 5 and 4. Their product ends in 0 (5 * 4 = 20). Step 6: If the product's last digit is zero and it is to the extreme right of the decimal point, it is usually not counted as a significant decimal place unless specified. Step 7: Since the product ends in a '0' due to 5 * 4 = 20, that '0' at the extreme right of the decimal point will not be considered a significant digit. Step 8: Therefore, the number of significant digits to the right of the decimal point will be 7 - 1 = 6.

Solution: Step 1: To convert a fraction to a decimal, perform the division of the numerator by the denominator. Step 2: Divide 1999 by 2111. Step 3: 1999 ÷ 2111 ≈ 0.946944... Step 4: Rounding to three decimal places (as suggested by options), the value is 0.946.

Solution: Step 1: Rewrite the expression to simplify decimals by multiplying by powers of 10: Numerator: 0.0203 * 2.92 = (203 / 10000) * (292 / 100) = (203 * 292) / 1000000 Denominator: 0.0073 * 14.5 * 0.7 = (73 / 10000) * (145 / 10) * (7 / 10) = (73 * 145 * 7) / 1000000 Step 2: The expression becomes [(203 * 292) / 1000000] / [(73 * 145 * 7) / 1000000]. Step 3: Cancel out the 1000000 from both numerator and denominator. Step 4: The simplified expression is (203 * 292) / (73 * 145 * 7). Step 5: Perform divisions: 203 / 7 = 29 292 / 73 = 4 145 / 29 = 5 Step 6: Substitute these simplified values back: (29 * 4) / (1 * 5 * 1). Step 7: Calculate the final result: 116 / 5 = 23.2. (Correction from problem, solution provided 4/5 = 0.8; I need to recheck the provided solution logic) Rechecking solution provided: `0.0203 × 2.92 / 0.0073 × 14.5 × 0.7 = 203 × 292 / 73 × 145 × 7`. This implies `(0.0203/0.0073) * (2.92/14.5) * (1/0.7)`. This is not how the provided calculation works. Let's re-evaluate based on the provided solution. It effectively multiplies the numerator and denominator by 10^7. (0.0203 × 2.92) / (0.0073 × 14.5 × 0.7) = (203 × 292) / (73 × 145 × 7) (This step implies multiplying numerator and denominator by 10^7 and carefully placing the decimal points to clear them). Step 5 (Revised): Now simplify the expression (203 × 292) / (73 × 145 × 7): Recognize that 203 = 7 × 29. Recognize that 73 is a prime number. Recognize that 292 = 4 × 73. Recognize that 145 = 5 × 29. Step 6 (Revised): Substitute these factors: = (7 × 29 × 4 × 73) / (73 × 5 × 29 × 7) Step 7 (Revised): Cancel common factors (7, 29, 73): = 4 / 5 Step 8 (Revised): Convert the fraction to a decimal: 4 / 5 = 0.8.

Solution: Step 1: Perform the multiplication in the numerator: 3.5 * 1.4 = 4.9. Step 2: Now perform the division: 4.9 / 0.7. Step 3: To simplify the division, multiply both numerator and denominator by 10 to remove decimals: 49 / 7. Step 4: Calculate the final result: 49 / 7 = 7.

Solution: Step 1: Round each number to a convenient value for estimation. 3.157 ≈ 3.2 4126 ≈ 4100 (or keep as 4126 for precision in numerator) 3.198 ≈ 3.2 63.972 ≈ 64 2835.121 ≈ 2835 (or 2800 for rough estimation) Step 2: Substitute the rounded values into the expression: (3.2 * 4126 * 3.2) / (64 * 2835) Step 3: Perform multiplication in the numerator: 3.2 * 3.2 = 10.24. So, (10.24 * 4126) / (64 * 2835). Step 4: Continue simplifying. Notice 64 is a multiple of 3.2 (64 = 20 * 3.2). So, (3.2 * 4126 * 3.2) / (20 * 3.2 * 2835) = (3.2 * 4126) / (20 * 2835). Step 5: Further simplification: (3.2 / 20) * (4126 / 2835) = 0.16 * 1.455 (approx). Step 6: Calculate 0.16 * 1.455 ≈ 0.2328. Step 7: The closest option to 0.2328 is 0.2.

Solution: Step 1: From the given information, 168 * 32 = 5376, we can deduce that 5376 / 168 = 32. Step 2: Now consider the expression to be evaluated: 5.376 / 16.8. Step 3: We can rewrite this as (5376 / 1000) / (168 / 10). Step 4: This simplifies to (5376 / 168) * (10 / 1000). Step 5: Substitute the known division from Step 1: 32 * (1 / 100). Step 6: Calculate the final result: 32 / 100 = 0.32.

Solution: Step 1: Convert all mixed fractions to improper fractions. 7 1/2 = 15/2 2 1/4 = 9/4 1 1/4 = 5/4 1 1/2 = 3/2 Step 2: Start with the innermost parenthesis: (3/2 - 1/3 - 1/6). Find a common denominator, which is 6: (9/6 - 2/6 - 1/6) = (9 - 2 - 1) / 6 = 6/6 = 1. Step 3: Substitute this back into the expression: 15/2 - [9/4 ÷ {5/4 - 1/2 * (1)}]. Step 4: Simplify inside the curly braces: {5/4 - 1/2 * 1} = {5/4 - 1/2}. Find a common denominator, which is 4: {5/4 - 2/4} = 3/4. Step 5: Substitute this back: 15/2 - [9/4 ÷ 3/4]. Step 6: Perform the division inside the square brackets: 9/4 ÷ 3/4 = 9/4 * 4/3. Cancel out 4 and simplify 9/3: 3. Step 7: Substitute back: 15/2 - 3. Step 8: Find a common denominator for subtraction: 15/2 - 6/2 = (15 - 6) / 2. Step 9: The final result is 9/2. Step 10: Convert back to a mixed fraction: 9/2 = 4 and 1/2.

Solution: Step 1: Recognize the given number as a mixed fraction, which can be written as 101 + 27/100000. Step 2: Convert the fractional part 27/100000 to a decimal. Dividing by 100000 means moving the decimal point 5 places to the left. So, 27/100000 = 0.00027. Step 3: Add the integer part to the decimal part: 101 + 0.00027. Step 4: The result is 101.00027.

Solution: Step 1: Multiply the numbers as if they were whole numbers, ignoring the decimal points temporarily: 477 * 124 * 86. Step 2: First, 477 * 124 = 59148. Step 3: Next, 59148 * 86 = 5086728. Step 4: Count the total number of decimal places in the original numbers. 47.7 has 1 decimal place. 12.4 has 1 decimal place. 8.6 has 1 decimal place. Step 5: The total number of decimal places is 1 + 1 + 1 = 3. Step 6: Place the decimal point 3 places from the right in the product obtained in Step 3. 5086728 becomes 5086.728. Step 7: The final product is 5086.728.

Solution: Step 1: Calculate the first multiplication: 5 * 1.6 = 8. Step 2: Calculate the second multiplication: 2 * 1.4 = 2.8. Step 3: Perform the subtraction in the numerator: 8 - 2.8 = 5.2. Step 4: Perform the division: 5.2 / 1.3. Step 5: To simplify division, multiply numerator and denominator by 10: 52 / 13. Step 6: Calculate the final result: 52 / 13 = 4.