- The number of stars in a small galaxy is estimated to be "three hundred million, five hundred thousand, two hundred." Which of the following shows this number written correctly in expanded form?
Answer: 300,000,000 + 500,000 + 200
First, write the number in standard form: "three hundred million, five hundred thousand, two hundred" is 300,500,200. In expanded form, this number is the sum of the values of its digits: 300,000,000 + 500,000 + 200.
- In the number represented by "seven hundred three thousand, one hundred ninety-four," what is the value of the digit 3?
Answer: 3,000
First, write the number in standard form: 703,194. The digit 3 is in the thousands place. Therefore, its value is 3 × 1,000, which is 3,000.
- A charity drive collected a total of "one million, two hundred thousand" pennies. If there are one hundred pennies in a dollar, how many dollars were collected?
Answer: 12,000
First, write the total number of pennies in standard form: "one million, two hundred thousand" is 1,200,000. To find the number of dollars, divide the total number of pennies by 100: 1,200,000 ÷ 100 = 12,000.
- The attendance at a major sporting event was announced as "fifty thousand, six hundred two." Which digit is in the tens place of this number?
Answer: 0
First, convert the number from words to standard form. "Fifty thousand, six hundred two" is written as 50,602. The places are ten thousands (5), thousands (0), hundreds (6), tens (0), and ones (2). The digit in the tens place is 0.
- A number is written as "eighty-four thousand, two hundred five." A new number is formed by swapping the digit in the thousands place with the digit in the tens place. What is the new number in standard form?
Answer: 80,245
First, write the original number in standard form: "eighty-four thousand, two hundred five" is 84,205. The digit in the thousands place is 4. The digit in the tens place is 0. Swapping these two digits gives the new number 80,245.
- What is the product of "two hundred five" and "one hundred"?
Answer: 20,500
First, write "two hundred five" in standard form, which is 205. Next, write "one hundred" in standard form, which is 100. The product is the result of multiplying these two numbers: 205 × 100 = 20,500.
- A stadium has a capacity of forty-five thousand, six hundred people. On game day, the attendance was forty-three thousand, eight hundred. How many empty seats were there?
Answer: 1,800
First, write the capacity and attendance in standard form. Capacity: 45,600. Attendance: 43,800. To find the number of empty seats, subtract the attendance from the capacity: 45,600 - 43,800 = 1,800.
- A scientist measured the width of a specimen to be "four and thirty-two thousandths" centimeters. How is this measurement written in standard form?
Answer: 4.032
In word form for numbers with decimals, the word "and" represents the decimal point. "Four" is the whole number part. "Thirty-two thousandths" means the last digit of 32 should be in the thousandths place (the third place after the decimal). This is written as 0.032. Combining the whole number and the decimal part gives 4.032.
- A school buys one hundred twenty boxes of crayons. Each box contains "one hundred forty-four" crayons. What is the total number of crayons the school purchased?
Answer: 17,280
First, write the number of crayons per box in standard form: "one hundred forty-four" is 144. To find the total number of crayons, multiply the number of boxes by the number of crayons per box: 120 × 144 = 17,280.
- A video game company sold six million, twenty thousand, three hundred copies of its most popular game. How is this number written in standard form?
Answer: 6,020,300
To write "six million, twenty thousand, three hundred" in standard form, break it down by place value. The millions place has a 6. The thousands period has "twenty," so there is a 2 in the ten thousands place and a 0 in the thousands place. The hundreds place has a 3. All other places are filled with zeros as placeholders. This gives 6,020,300.
- A bank vault contains one hundred fifty thousand, thirty-six dollars. If a security guard removes one hundred dollars, how much money remains in the vault?
Answer: 149,936
First, write the amount of money in standard form: "one hundred fifty thousand, thirty-six" is 150,036. Then, subtract the one hundred dollars that were removed: 150,036 - 100 = 149,936.
- A city's population is two hundred fifty thousand, ninety-six. A neighboring city has a population that is one thousand less. What is the population of the neighboring city?
Answer: 249,096
First, write the city's population in standard form: "two hundred fifty thousand, ninety-six" is 250,096. The problem states the neighboring city has one thousand less, so subtract 1,000 from this number. 250,096 - 1,000 = 249,096.
- A website had nine hundred ninety-nine thousand, nine hundred five visitors in one month. The next month, the number of visitors increased by one hundred. What was the number of visitors in the next month?
Answer: 1,000,005
First, write the initial number of visitors in standard form: "nine hundred ninety-nine thousand, nine hundred five" is 999,905. The number increased by one hundred, so add 100: 999,905 + 100 = 1,000,005.
- The distance from Earth to the Sun is approximately one hundred forty-nine million, six hundred thousand kilometers. What is this number rounded to the nearest million kilometers?
Answer: 150,000,000
First, write the number in standard form: 149,600,000. To round to the nearest million, look at the digit in the hundred thousands place, which is 6. Since 6 is 5 or greater, round up the digit in the millions place (9). Rounding up 149 million gives 150 million. So, the rounded number is 150,000,000.
- A number is described as having seven hundred thousands, eight tens, and two ones. How is this number written in standard form?
Answer: 700,082
This number is built from its place values. "Seven hundred thousands" is 700,000. "Eight tens" is 80. "Two ones" is 2. Adding these values together gives 700,000 + 80 + 2 = 700,082.
- A farmer has three fields. The first produced "three thousand, five hundred" bushels of corn. The second produced "four thousand, two hundred" bushels. The third produced "one thousand, eight hundred" bushels. What was the total number of bushels produced?
Answer: 9,500
First, write the production of each field in standard form: 3,500, 4,200, and 1,800. To find the total, add these three numbers: 3,500 + 4,200 + 1,800 = 9,500.
- Four contestants competed in a read-a-thon. Alex read for twelve thousand, six hundred ten minutes. Beth read for twelve thousand, sixty-one minutes. Carlos read for twelve thousand, one hundred six minutes. Dana read for twelve thousand, six hundred one minutes. Who read for the longest amount of time?
Answer: Alex
First, write each person's time in standard form:
Alex: 12,610 minutes
Beth: 12,061 minutes
Carlos: 12,106 minutes
Dana: 12,601 minutes
Comparing these four numbers, 12,610 is the largest. Therefore, Alex read for the longest amount of time.
- An ancient manuscript is dated to the year written as "one thousand, four hundred ninety-two." What is the sum of the digits of this year?
Answer: 16
First, convert the year from words to standard form. "One thousand, four hundred ninety-two" is 1492. Next, find the sum of its digits: 1 + 4 + 9 + 2 = 16.
- A factory produced sixteen thousand, seventy-one parts in March and sixty thousand, seventeen parts in April. What is the standard form for the number of parts produced in April?
Answer: 60,017
The question asks for the number of parts produced in April. The number given for April is "sixty thousand, seventeen." In standard form, this is written as 60,017. The number for March, 16,071, is a distractor.
- What number is halfway between "nine thousand, eight hundred" and "ten thousand, two hundred"?
Answer: 10,000
First, write the two numbers in standard form: 9,800 and 10,200. To find the number halfway between them, you can find their average. Add the numbers: 9,800 + 10,200 = 20,000. Then divide by 2: 20,000 ÷ 2 = 10,000.
