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3. Some digits and their places in the number are given below. Write down the numbers they make.

For example, [tex]$5 TTh, 2 Th, 3 H, 2 T, 1 U = 52,321$[/tex]; [tex]$9 H, 8 Th, 5 U = 80,905$[/tex].

(1) [tex]$7 U, 2 T, 5 Th, 9 Th$[/tex]

(2) [tex]$3 H, 4 Th, 5 T, 1 TTh$[/tex]

(3) [tex]$5 T, 8 Th, 7 TTh$[/tex]

(4) [tex]$5 Th, 7 TTh, 3 H, 2 T, 4 U$[/tex]



Answer :

GinnyAnswer
To write down the numbers made from the given digits and their places, we will combine the values, ensuring that we properly account for each place (units, tens, hundreds, thousands, ten thousands, etc.). Let's solve each part step-by-step:

### (1) Digits: [tex]\(7\)[/tex] units ([tex]\(U\)[/tex]), [tex]\(2\)[/tex] tens ([tex]\(T\)[/tex]), [tex]\(5\)[/tex] thousands ([tex]\(Th\)[/tex]), [tex]\(9\)[/tex] thousands ([tex]\(Th\)[/tex])

For this, we notice that there are two different values given for the thousands place, [tex]\(5 Th\)[/tex] and [tex]\(9 Th\)[/tex]. The last mentioned value, [tex]\(9 Th\)[/tex], overrides the previous one, hence we use [tex]\(9 Th\)[/tex].

1. Thousand place: [tex]\(9 \times 1000 = 9000\)[/tex]
2. Tens place: [tex]\(2 \times 10 = 20\)[/tex]
3. Units place: [tex]\(7 \times 1 = 7\)[/tex]

Adding them together: [tex]\(9000 + 20 + 7 = 9027\)[/tex]

Number 1: [tex]\(9027\)[/tex]

### (2) Digits: [tex]\(3\)[/tex] hundreds ([tex]\(H\)[/tex]), [tex]\(4\)[/tex] thousands ([tex]\(Th\)[/tex]), [tex]\(5\)[/tex] tens ([tex]\(T\)[/tex]), [tex]\(1\)[/tex] ten thousands ([tex]\(TTh\)[/tex])

1. Ten thousand place: [tex]\(1 \times 10000 = 10000\)[/tex]
2. Thousand place: [tex]\(4 \times 1000 = 4000\)[/tex]
3. Hundreds place: [tex]\(3 \times 100 = 300\)[/tex]
4. Tens place: [tex]\(5 \times 10 = 50\)[/tex]

Adding them together: [tex]\(10000 + 4000 + 300 + 50 = 14350\)[/tex]

Number 2: [tex]\(14350\)[/tex]

### (3) Digits: [tex]\(5\)[/tex] tens ([tex]\(T\)[/tex]), [tex]\(8\)[/tex] thousands ([tex]\(Th\)[/tex]), [tex]\(7\)[/tex] ten thousands ([tex]\(TTh\)[/tex])

1. Ten thousand place: [tex]\(7 \times 10000 = 70000\)[/tex]
2. Thousand place: [tex]\(8 \times 1000 = 8000\)[/tex]
3. Tens place: [tex]\(5 \times 10 = 50\)[/tex]

Adding them together: [tex]\(70000 + 8000 + 50 = 78050\)[/tex]

Number 3: [tex]\(78050\)[/tex]

### (4) Digits: [tex]\(5\)[/tex] thousands ([tex]\(Th\)[/tex]), [tex]\(7\)[/tex] ten thousands ([tex]\(TTh\)[/tex]), [tex]\(3\)[/tex] hundreds ([tex]\(H\)[/tex]), [tex]\(2\)[/tex] tens ([tex]\(T\)[/tex]), [tex]\(4\)[/tex] units ([tex]\(U\)[/tex])

1. Ten thousand place: [tex]\(7 \times 10000 = 70000\)[/tex]
2. Thousand place: [tex]\(5 \times 1000 = 5000\)[/tex]
3. Hundreds place: [tex]\(3 \times 100 = 300\)[/tex]
4. Tens place: [tex]\(2 \times 10 = 20\)[/tex]
5. Units place: [tex]\(4 \times 1 = 4\)[/tex]

Adding them together: [tex]\(70000 + 5000 + 300 + 20 + 4 = 75324\)[/tex]

Number 4: [tex]\(75324\)[/tex]

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